M = \(\dfrac{2018a}{ab+2018a+2018}+\dfrac{b}{bc+b+2018}+\dfrac{c}{ac+c+1}\)
M = \(\dfrac{a^2bc}{ab+a^2bc+abc}+\dfrac{b}{bc+b+abc}+\dfrac{c}{ac+c+1}\)
M = \(\dfrac{a^2bc}{ab\left(ac+c+1\right)}+\dfrac{b}{b\left(ac+c+1\right)}+\dfrac{c}{ac+c+1}\)
M= \(\dfrac{ac}{ac+c+1}+\dfrac{1}{ac+c+1}+\dfrac{c}{ac+c+1}\)
M = \(\dfrac{ac+c+1}{ac+c+1}\)
M = 1